Let be an acute angled triangle with centroid and the internal bisectors of angles…

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Three-Dimensional Geometry

Problem

Let

ABC

be an acute angled triangle with centroid

G

and the internal bisectors of angles

A, B

and

C

meets

BC, CA

and

AB

M, N

and

K

respectively using vectors, prove that if

G

lies on one of the sides of

\Delta MNK

, then one of the altitudes of

\Delta ABC

equals the sum of other two.